[mxplxxx (OP)]

What is the force (of gravity) exerted by the sun on the earth. Is this enough to keep the earth in a circular orbit around the sun. What about Jupiter?  How come Mars weighs less than the earth but is further from the sun? How come satellites stay in orbit and not plummet to earth due to the force of the earths gravity.

On a related topic, am I lighter when traveling in a plane?

On yet another related topic, is something weightless at the center of the earth. I read somewhere that the sun's fusion starts because of the gravity its center. Is this so? It seem to me the fusion is likely because of the particles near the center losing kinetic energy as they slow.

[PmbPhy]

What is the force (of gravity) exerted by the sun on the earth.

If M is the mass of the Sun, m is the mass of the Earth, r is the distance from the Earth to the Sun, F is the force on the Earth by the Sun and F is magnitude of F then

F = GMm/r²

Is this enough to keep the earth in a circular orbit around the sun.

Yes. However the Earth isn't in a circular orbit around the Sun. The orbit is an ellipse with the Sun at one foci.

What about Jupiter?

What about it? The same kind of relationship holds.

  How come Mars weighs less than the earth but is further from the sun?

What do you mean? The term weight has been defined in two separate ways in the physics literature. It can be said that if the only force on an object is a gravitational force then one definition defines its weight as equaling the gravitational force while the other definition defines it as being weightless (e.g. astronauts in the ISP are in free-fall and consider themselves to be weightless in their frame of reference.

How come satellites stay in orbit and not plummet to earth due to the force of the earths gravity.

Because their inertia tries to keep them moving in a straight line while the gravitational force tries to accelerate them to the Earth's center. The end result is the satellite falling around the Earth. Think about a cannonball being fired from a cannon which is pointed parallel to the Earth's surface. The faster the cannonball's speed the further out it will land. If the speed is large enough it will "fall" around the Earth.

On a related topic, am I lighter when traveling in a plane?

No. At least not significantly. Since planes fly above the Earth's surface the value of r is larger making F smaller. But the difference is so small that it can be ignored. In fact it'd be extremely hard to measure any difference in weight.

On yet another related topic, is something weightless at the center of the earth.

Yes.

I read somewhere that the sun's fusion starts because of the gravity its center. Is this so?

Not just at the center. Fusion occurs in a much larger region of the Sun than just at the Sun's center.

It seem to me the fusion is likely because of the particles near the center losing kinetic energy as they slow.

That's not the reason. Actually the opposite is true. The pressure inside the Sun is so high that the nuclei are basically "squeezed" together. This occurs because the nuclei have greater kinetic energy, enough to overcome the Coulomb barrier. There are also quantum mechanical considerations which play apart in the fusion of Helium nuclei. If you wish to learn more about all of this then I recommend looking it up on Wikipedia.

[mxplxxx (OP)]

RE the center of the earth, it seems to me that a particle there will be be pulled apart by the force of gravity being exerted equally on all sides by all the other particles that make up the earth.

[jeffreyH]

RE the center of the earth, it seems to me that a particle there will be be pulled apart by the force of gravity being exerted equally on all sides by all the other particles that make up the earth.

It is more likely to be compressed. Otherwise black hole formation couldn't happen.

[mxplxxx (OP)]

RE the center of the earth, it seems to me that a particle there will be be pulled apart by the force of gravity being exerted equally on all sides by all the other particles that make up the earth.

It is more likely to be compressed. Otherwise black hole formation couldn't happen.

Thx for your contribution. "Compressed", how? Maybe a black hole is just absence of space into which space is pouring (maybe a new universe in progress) !

[evan_au]

RE the center of the earth, it seems to me that a particle there will be be pulled apart by the force of gravity being exerted equally on all sides by all the other particles that make up the earth.

This is incorrect, Mr mxplxxx.

Isaac Newton showed that the gravitational forces from the distributed mass of the Earth exactly balance at the center of the Earth.
- So there will be no force pulling matter apart
- However, there is all that pressure from the surrounding mass of the Earth squashing down on you (as Jeffrey suggests)
- But if you were able to somehow build a little bubble at the center of the Earth, strong enough to resist all that heavy rock, your particle at the center of the Earth would float freely, with nothing compressing it, and nothing pulling it apart.

Of course, Isaac Newton had to invent a whole new branch of mathematics to come to that conclusion (his contemporary Gottfried Leibniz also developed calculus at about the same time).

[mxplxxx (OP)]

Isaac Newton showed that the gravitational forces from the distributed mass of the Earth exactly balance at the center of the Earth.

Can you give me a reference for this please.

[evan_au]

Isaac Newton showed that the gravitational forces from the distributed mass of the Earth exactly balance at the center of the Earth.

Can you give me a reference for this please.

See: https://en.wikipedia.org/wiki/Shell_theorem

[mxplxxx (OP)]

Isaac Newton showed that the gravitational forces from the distributed mass of the Earth exactly balance at the center of the Earth.

Can you give me a reference for this please.

See: https://en.wikipedia.org/wiki/Shell_theorem

Thanks evan_au.

[jeffreyH]

Isaac Newton showed that the gravitational forces from the distributed mass of the Earth exactly balance at the center of the Earth.

Can you give me a reference for this please.

See: https://en.wikipedia.org/wiki/Shell_theorem

I hadn't realised that the Yukawa potential could be related to gravity. I have something to play with.

[mxplxxx (OP)]

So, it would seem that Newton's theories of gravity predict correct results but are not rooted in reality. The earth is not attracted to the sun via gravity, both warp the space (spacetime) around each other and travel in the lines of force that this warping generates (this seems to imply that gravity if just momentum acting along a line of force - is this a reasonable conclusion).

It could be argued that Newtons laws are digital simulations of the spacetime continuum and ditto for quantum theory. Possibly even these simulations also take place in our minds (and therefore that our minds are outside spacetime). A continuum, of course, can be approximated by splitting it up into points. The smaller the points, the closer the approximation.

[acsinuk]

 (this seems to imply that gravity if just momentum acting along a line of force - is this a reasonable conclusion).  What about the electromagnetic forces that spin the planets??

[Colin2B]

What about the electromagnetic forces that spin the planets?

The spin came from the rotation of the accretion disc, there is no continuing magnetic force making the planets spin or exerting force on the earth.

[acsinuk]

The WMAP results seem to suggest that we a missing a really large dark force.  So if its not magnetic perhaps its electrostatic but our instruments cant sense it?

[evan_au]

The WMAP results seem to suggest that we a missing a really large dark force.

This is significant on cosmic scales, but is (currently) insignificant on the scale of our Solar System or our galaxy.

This mysterious force has been dubbed Dark Energy. So it is no longer missing, but giving it a name doesn't make it any less mysterious.

So if its not magnetic perhaps its electrostatic but our instruments cant sense it?

We now have quite sensitive instruments that can detect electrostatic forces, so if electrostatics were significant at the level of the Solar system we would detect it.

If the electrostatics were only significant at cosmic scales (eg slightly more electrons than protons in the universe, for example) then we probably would not detect it on Earth.

However, this still does not explain the rate of cosmic inflation in the early universe, which we also infer from surveys like WMAP.

[mxplxxx (OP)]

The earth is not attracted to the sun via gravity, both warp the space (spacetime) around each other and travel in the lines of force that this warping generates

Why then does quantum theory predict the graviton particle to explain gravity? The graviton is a force particle with a ridiculously small value. How can this puny particle mediate the (apparent) attraction of the sun and earth, particularly when the force it exerts is inversely propositional to the square of the distance between two bodie ?

[evan_au]

The graviton is a force particle with a ridiculously small value.

...and Gravity is a force which is ridiculously weak (compared to electromagnetism or the strong nuclear force).

At this stage, the graviton is merely hypothetical, an analogy; there is no experimental evidence for it.
The sole claim to fame for string theory is that it combines general relativity and the graviton in a natural way; it's a pity it can't prove anything at the moment.

How can this puny particle mediate the (apparent) attraction of the sun and earth, particularly when the force it exerts is inversely propositional to the square of the distance between two bodies ?

In theory, it takes a large number of gravitons to mediate the attraction between Sun and Earth.

In principle, the mechanism is not radically different from photons which mediate the electromagnetic force, which also follows an inverse square law.

See: https://en.wikipedia.org/wiki/Graviton

[mxplxxx (OP)]

(this seems to imply that gravity if just momentum acting along a line of force - is this a reasonable conclusion).

Where does the momentum come from when I jump up and down? It may be from our (near) absolute momentum. We are part of the Earth frame of reference but also part of many other frames of reference. A universe-level observer sees us whizzing around the universe as part of many structures (solar system etc.) under the influence of gravity. We are slowing down at one point or accelerating at another point or become stationary at yet another point and pretty much changing direction all the time. When we jump up and down I am guessing we temporarily leave our earth frame of reference and come under the influence of our absolute momentum. It is possible that it is this momentum that causes us to come back to earth.

It is worth noting that our absolute momentum and  membership of a hierarchy of frames of reference  (molecule, solar system, galaxy etc.) puts constraints on the way the universe can evolve structurally and energetically which may have gravity-related consequences.   

[evan_au]

We are part of the Earth frame of reference but also part of many other frames of reference.

As I understand it, there is a special place in Special Relativity for an "Inertial" frame of reference. Bodies in an inertial frame of reference will travel in a straight line at constant velocity, with no acceleration. Effectively when you are weightless, far from any source of gravity (mass).
- You, standing on the Earth, are not in an inertial frame of reference (not weightless; the path of a pendulum is slightly curved by the rotation of the Earth).
- The Earth, orbiting around the Sun is not in an inertial frame of reference (weightless, but the path is slightly curved by the mass of the Sun)
- The Sun, orbiting around the galaxy is not in an inertial frame of reference (weightless, but the path is even more subtly curved by the mass of the galaxy)

However, when you jump, you become weightless (for a short time).
- And if you consider a small volume around yourself, for the small amount of time while you are weightless, you can approximate this by an inertial frame of reference.
- For example, juggling becomes impossible, because the balls now travel in straight lines (relative to you).

When we jump up and down I am guessing we temporarily leave our earth frame of reference and come under the influence of our absolute momentum.

There is no such things as "absolute momentum". Your actual momentum will differ depending on which frame of reference it is measured in.
In the (almost) inertial frame of reference which is you jumping, you have zero momentum.

We are slowing down at one point or accelerating at another point or become stationary at yet another point and pretty much changing direction all the time.

General Relativity takes into account the effects of mass, and you can select frames of reference rather arbitrarily. But depending on what you are trying to calculate (and how accurately you are trying to calculate it), some frames of reference are easier to use than others.

[acsinuk]

The frame of reference used to be the centre of the earth, then the centre of the sun but now it is the centre of our galaxy in Sagittarius A* the magnetic black hole hub of our galaxy.  How does relativity explain the moving of the stars around that hub without electromagnetism??